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10.59 To tip or not to tip. A study of tipping behaviors examined the relationship between the color of the shirt worn by the server and whether the customer left a tip.12 There were 418 male customers in the study; 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the 349 who were served by a server wearing a different colored shirt, 130 left a tip. a. Find the proportion of tippers for the red-shirted servers and the proportion of tippers for the servers with other colored shirts. b. Find a 95% confidence interval for the difference in proportions. à. Give a null hypothesis for this setting in terms of the parameters. Explain the meaning of the null hypothesis in simple terms. b. Give an alternative hypothesis for this setting in terms of the parameters. Explain the meaning of the alternative hypothesis in simple terms. Give a reason for your choice of this particular alternative hypothesis. c. Are the conditions satisfied for the use of the significance test based on the Normal distribution? Explain your answer.

10.59 To tip or not to tip. A study of tipping behaviors examined the relationship between the color of the shirt worn by the server and whether the customer left a tip.12 There were 418 male customers in the study; 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the 349 who were served by a server wearing a different colored shirt, 130 left a tip. a. Find the proportion of tippers for the red-shirted servers and the proportion of tippers for the servers with other colored shirts. b. Find a 95% confidence interval for the difference in proportions. à. Give a null hypothesis for this setting in terms of the parameters. Explain the meaning of the null hypothesis in simple terms. b. Give an alternative hypothesis for this setting in terms of the parameters. Explain the meaning of the alternative hypothesis in simple terms. Give a reason for your choice of this particular alternative hypothesis. c. Are the conditions satisfied for the use of the significance test based on the Normal distribution? Explain your answer.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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10.59 To tip or not to tip. A study of tipping behaviors examined the relationship between the color of the shirt worn by the server and whether the customer left a tip. 12 There were 418 male customers in the study; 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the 349 who were served by a server wearing a different colored shirt, 130 left a tip. a. Find the proportion of tippers for the red-shirted servers and the proportion of tippers for the servers with other colored shirts. b. Find a 95% confidence interval for the difference in proportions. a. Give a null hypothesis for this setting in terms of the parameters. Explain the meaning of the null hypothesis in simple terms. b. Give an alternative hypothesis for this setting in terms of the parameters. Explain the meaning of the alternative hypothesis in simple terms. Give a reason for your choice of this particular alternative hypothesis. c. Are the conditions satisfied for the use of the significance test based on the Normal distribution? Explain your answer. a. What is the distribution of the test statistic if the null hypothesis is true? b. Find the test statistic. c. Find the P-value. d. Use a sketch of a Normal distribution to explain the interpretation of the P-value that you found in part (c).
Transcribed Image Text:10.59 To tip or not to tip. A study of tipping behaviors examined the relationship between the color of the shirt worn by the server and whether the customer left a tip. 12 There were 418 male customers in the study; 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the 349 who were served by a server wearing a different colored shirt, 130 left a tip. a. Find the proportion of tippers for the red-shirted servers and the proportion of tippers for the servers with other colored shirts. b. Find a 95% confidence interval for the difference in proportions. a. Give a null hypothesis for this setting in terms of the parameters. Explain the meaning of the null hypothesis in simple terms. b. Give an alternative hypothesis for this setting in terms of the parameters. Explain the meaning of the alternative hypothesis in simple terms. Give a reason for your choice of this particular alternative hypothesis. c. Are the conditions satisfied for the use of the significance test based on the Normal distribution? Explain your answer. a. What is the distribution of the test statistic if the null hypothesis is true? b. Find the test statistic. c. Find the P-value. d. Use a sketch of a Normal distribution to explain the interpretation of the P-value that you found in part (c).
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